If you're booking with an agency, airline, or international travel website, you'll be quoted the cost in your own currency and the total shouldn't change: you pay exactly what is quoted when you book. But if you book anything direct in local currency, with a balance to settle at the end of the trip, be wary of how the constant changes in exchange rate could affect the total cost of your trip. This may not be much if you're staying in hostels or budget accommodation, but if you're booking luxury accommodation, a drop in the value of the pound could increase the cost of the trip by hundreds of pounds.
Image Source: POPSUGAR Photography / Mark Popovich